You don't need visa.
US citizens don't need to apply for visa to enter Jordan, Israel and Egypt. These countries are free to enter, or you pay visa-fee at the airport after your arrival to their country.

If you are traveling to Ukraine in winter, you definetly need to bring warm clothes. And keep in mind, that it might be really cold especially in January and February (-10...-25 degrees) and in March it is still cold, -5...0 degrees), might be windy…